1. Field of the Invention
The present invention relates to optical transmission apparatuses and, more specifically, to an optical transmission apparatus using an external optical modulator. The apparatus is capable of controlling a bias voltage applied to the external optical modulator for making the bias voltage follow a shift in optimal bias voltage caused by DC drift.
2. Description of the Background Art
In optical transmission apparatuses used in conventional optical communications systems, conventionally adopted is a modulation scheme of directly modulating an electric current fed to a laser diode constructing a light source with an input signal and outputting an optical signal modulated with the input signal. In this modulation scheme, the current fed to the laser diode changes, and therefore, an optical signal from the laser diode changes in oscillation wavelength due to its chirp characteristics. If transmitted over a long distance, the optical signal outputted from such laser diode is deteriorated in waveform under the influence of chromatic dispersion within an optical fiber.
For future mobile communications, high frequencies, especially, extremely high frequencies (millimeter-wave band), will be used for substantially increasing transmission rate, because band reservation can be made easily in these frequencies. However, if signals in the millimeter-wave band are transmitted through a coaxial cable, a large loss will be caused. Thus, in this case, amplifiers are required at several tens-of-millimeter intervals. This requirement poses problems in view of cost and reliability for actual system configuration. Therefore, for millimeter-wave band signal transmission, use of optical fibers with less transmission loss is required. However, laser diodes now commercially available have frequency response characteristics of around 10 GHz, and thus cannot respond to signals of extremely high frequency. For this reason, such laser diodes cannot be directly modulated by the millimeter-wave signals.
Therefore, for long-distance transmission or transmission of signals of high frequency such as millimeter waves, an optical transmission apparatus having a Mach-Zehnder-type external optical modulator is, in principle, less prone to cause chirp and capable of responding to signals of higher frequency has been suggested for use.
FIG. 11 shows the structure of a Mach-Zehnder-type external optical modulator (hereinafter referred to as MZ-type optical modulator). An optical carrier outputted from a light source is provided to the MZ-type optical modulator, and branched to two optical waveguides. When a voltage is applied to electrodes provided on a crystal substrate to cause an electric field, the index of refraction in the waveguides is changed. As a result, the lights propagated through the waveguides are changed in phase. Note that shown in FIG. 11 is such structure that only the light through one optical waveguide is phase-modulated. The lights from these optical waveguides are combined with each other, and outputted as an optical signal from a MZ-type optical modulator. The optical electric field of the outputted optical signal is represented by the following equation (1).                                                                                           E                                      Ex                    -                    Mod                                                  ⁡                                  (                                      V                    ,                    t                                    )                                            =                              xe2x80x83                            ⁢                                                                    1                                          2                                                        ⁢                  exp                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          ⅈ                      ⁢                                              xe2x80x83                                            ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                                        )                                                  +                                                      1                                          2                                                        ⁢                                      expⅈ                    ⁡                                          [                                              {                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                      φ                            ⁡                                                          (                                                              V                                ,                                t                                                            )                                                                                                      }                                            ]                                                                                                                                              =                              xe2x80x83                            ⁢                                                                    1                                          2                                                        ⁢                  exp                  ⁢                                      {                                          ⅈ                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                                                    φ                              ⁡                                                              (                                                                  V                                  ,                                  t                                                                )                                                                                      2                                                                          )                                                              }                                    ⁢                  exp                  ⁢                                      {                                          -                                                                        ⅈφ                          ⁡                                                      (                                                          V                              ,                              t                                                        )                                                                          2                                                              }                                                  +                                                                                                        xe2x80x83                            ⁢                                                1                                      2                                                  ⁢                exp                ⁢                                  xe2x80x83                                ⁢                                  {                                      ⅈ                    ⁡                                          (                                                                        ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              φ                            ⁡                                                          (                                                              V                                ,                                t                                                            )                                                                                2                                                                    )                                                        }                                ⁢                exp                ⁢                                  xe2x80x83                                ⁢                                  {                                                            ⅈ                      ⁢                                              xe2x80x83                                            ⁢                                              φ                        ⁡                                                  (                                                      V                            ,                            t                                                    )                                                                                      2                                    }                                                                                                        =                              xe2x80x83                            ⁢                                                1                                      2                                                  ⁢                exp                ⁢                                  xe2x80x83                                ⁢                                                      {                                          ⅈ                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                                                    φ                              ⁡                                                              (                                                                  V                                  ,                                  t                                                                )                                                                                      2                                                                          )                                                              }                                    [                                                            exp                      ⁢                                              {                                                  -                                                                                    ⅈφ                              ⁡                                                              (                                                                  V                                  ,                                  t                                                                )                                                                                      2                                                                          }                                                              +                                                                                                                                          xe2x80x83                            ⁢                                                exp                  ⁢                                      xe2x80x83                                    ⁢                                      {                                                                  ⅈ                        ⁢                                                  xe2x80x83                                                ⁢                                                  φ                          ⁡                                                      (                                                          V                              ,                              t                                                        )                                                                                              2                                        }                                                  ]                                                                                        =                              xe2x80x83                            ⁢                                                                    2                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      {                                                                  φ                        ⁡                                                  (                                                      V                            ,                            t                                                    )                                                                    /                      2                                        }                                    ⁢                  exp                  ⁢                                      {                                          ⅈ                      (                                                                        ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              φ                            ⁡                                                          (                                                              V                                ,                                t                                                            )                                                                                2                                                                                                                    }                                                                        (        1        )            
provided that                                                                         φ                ⁡                                  (                                      V                    ,                    t                                    )                                            =                                                                    φ                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    V                    )                                                  +                                                      φ                    RF                                    ⁡                                      (                    t                    )                                                                                                                          =                                                                    φ                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    V                    )                                                  +                                  m                  ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    f                                    ⁢                  t                                                                                        (        2        )            
where V is a bias voltage, m is a phase modulation factor, and xcfx89f is angular frequency of an analog signal. By using this optical electric field, power of the optical signal outputted from the MZ-type optical modulator is given by the following equation (3).                                                                         P                out                            =                              xe2x80x83                            ⁢                                                                    E                                          Ex                      -                      Mod                                                        ⁡                                      (                                          V                      ,                      t                                        )                                                  xc3x97                                                      E                                          Ex                      -                      Mod                                        *                                    ⁡                                      (                                          V                      ,                      t                                        )                                                                                                                          =                              xe2x80x83                            ⁢                              2                ⁢                                                      cos                    2                                    ⁡                                      (                                                                  φ                        ⁡                                                  (                                                      V                            ,                            t                                                    )                                                                    /                      2                                        )                                                                                                                          =                              xe2x80x83                            ⁢                              S1                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      φ                    ⁡                                          (                                              V                        ,                        t                                            )                                                                                                                                              =                              xe2x80x83                            ⁢                              1                +                                  cos                  ⁡                                      (                                                                                            φ                          DC                                                ⁡                                                  (                          V                          )                                                                    +                                              m                        ⁢                                                  xe2x80x83                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                                                  ω                          f                                                ⁢                        t                                                              )                                                                                                                          =                              xe2x80x83                            ⁢                              1                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                                            φ                      DC                                        ⁡                                          (                      V                      )                                                        ⁢                                      cos                    ⁡                                          (                                              m                        ⁢                                                  xe2x80x83                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                                                  ω                          f                                                ⁢                        t                                            )                                                                      -                                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      φ                    ⁡                                          (                      V                      )                                                        ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          m                      ⁢                                              xe2x80x83                                            ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                                              ω                        f                                            ⁢                      t                                        )                                                                                                                          =                              xe2x80x83                            ⁢                              1                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                                            φ                      DC                                        ⁡                                          (                      V                      )                                                        ⁢                                      {                                                                                            J                          0                                                ⁡                                                  (                          m                          )                                                                    +                                              2                        ⁢                                                                              J                            2                                                    ⁡                                                      (                            m                            )                                                                          ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                      2                            ⁢                                                          ω                              f                                                        ⁢                            t                                                    )                                                                    +                      …                                        ⁢                                          xe2x80x83                                        }                                                  -                                                                                                        xe2x80x83                            ⁢                              sin                ⁢                                  xe2x80x83                                ⁢                                                      φ                    DC                                    ⁡                                      (                    V                    )                                                  ⁢                                  {                                                            2                      ⁢                                                                        J                          1                                                ⁡                                                  (                          m                          )                                                                    ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              ω                            f                                                    ⁢                          t                                                )                                                              +                                          2                      ⁢                                                                        J                          3                                                ⁡                                                  (                          m                          )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      3                            ⁢                                                          ω                              f                                                        ⁢                            t                                                    )                                                                                      +                    …                                    ⁢                                      xe2x80x83                                    }                                                                                        (        3        )            
At this time, a relation between a bias voltage and an optical output is shown in FIG. 12. In FIG. 12, the lateral axis represents the bias voltage, while the vertical axis represents optical output power. As such, the power of the optical signal outputted from the MZ-type optical modulator exhibits a sine-wave characteristic with respect to the bias voltage applied to the MZ-type optical modulator.
However, in the MZ-type optical modulator, the above relation between the bias voltage and the optical output may be varied with various conditions, such as time and temperature. Such phenomenon is called DC drift. This DC drift phenomenon is shown in FIG. 13.
Such DC drift phenomenon as shown in FIG. 13 causes a shift in phase state from an initial state. Accordingly, average power of the optical signal outputted from the MZ-type optical modulator is changed, thereby causing deterioration in signal characteristic. Note that the bias voltage at the initial phase state (where the amount of second order distortion caused by non-linearity of the external modulator is minimum) is hereinafter referred to as an optimal bias voltage (denoted by Vb in the drawing).
In the conventional optical transmission apparatus using the external optical modulator, the bias voltage applied to the external optical modulator is controlled based on the average power of the optical signal outputted from the external optical modulator so that the bias voltage can be made to follow the shift in the optimal bias voltage caused by DC drift. The average power can be calculated by converting the optical signal into an electrical signal and measuring DC components of the electrical signal, that is, electric power.
More specifically, in the initial state in which the bias voltage is optimally set, average power of the output optical signal is measured in advance, and stored as a reference value. Thereafter, the applied bias voltage is controlled so that the average power of the output optical signal agrees with the reference value.
However, compared with the shift in the applied bias voltage from the optimal bias voltage, a change in the average power of the output optical signal is extremely small. Therefore, it is very difficult to make the applied bias voltage accurately follow the shift in the optimal bias voltage based on the average power of the output optical signal.
Here, described is a relation between a shift in the applied bias voltage from the optimal bias voltage and a change in the average power of the output optical signal by using equations.
Average power of the output optical signal Pdc can be represented by the following equation (4) with the use of the result of the above equation (3).
Pdc=1+J0(m) cos (xcfx86(V))xe2x80x83xe2x80x83(4) 
In general, the optimal bias voltage is obtained when the initial phase state is xcfx80/2. If a change in phase caused by the bias voltage being shifted due to DC drift is xcfx86, the phase state at this time can be represented by the following equation (5).                               φ          ⁡                      (            V            )                          ⁢                  xe2x80x83                =                  xe2x80x83                ⁢                                            π              2                        ⁢                          xe2x80x83                        +                          xe2x80x83                        ⁢                          Ψ              ⁡                              (                V                )                                              ⁢                      xe2x80x83                    =                      xe2x80x83                    ⁢                                    π              2                        ⁢                          xe2x80x83                        +                          xe2x80x83                        ⁢                                          2                π                            ⁢                              xe2x80x83                            ⁢                              V                                  V                  π                                                                                        (        5        )            
From the above equations (4) and (5), the amount of change in the average power of the output optical signal with respect to the shift in the applied bias voltage from the optimal bias voltage can be obtained by the following equation (6).                                                                                           dP                                      d                    ⁢                                          xe2x80x83                                        ⁢                    c                                                  =                                                      J                    0                                    ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      φ                    ⁡                                          (                      V                      )                                                        ⁢                  d                  ⁢                                      xe2x80x83                                    ⁢                  φ                                                                                                        =                                                                            2                      ⁢                                              J                        0                                                              π                                    ⁢                                      1                    V                                    ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                                      φ                    ⁡                                          (                      V                      )                                                        ⁢                  d                  ⁢                                      xe2x80x83                                    ⁢                  φ                                                                    ⁢                  
                ⁢        where                            (        6        )                                          d          ⁢                      xe2x80x83                    ⁢          φ                =                              2            π                    ⁢                      1                          V              π                                ⁢          d          ⁢                      xe2x80x83                    ⁢          V                                    (        7        )            
An instantaneous shift in bias voltage caused by DC drift is extremely small. Therefore,                               φ          ⁡                      (            V            )                          ⁢                  xe2x80x83                ≈                  xe2x80x83                ⁢                  π          2                                    (        8        )            
and thus approximated at
sin xcfx86(V)≈0xe2x80x83xe2x80x83(9) 
As evident from the above, the change in the average power of the optical signal is extremely small with respect to the change in phase. Therefore, only a slightest change in the average power can be observed with respect to the shift in the applied bias voltage from the optimal bias voltage. It is thus difficult, as in the conventional art, to increase control accuracy if the bias voltage is controlled based on the average power of the output optical signal.
Low accuracy of controlling the bias voltage presents no problem for transmission of baseband digital signals. However, for transmission of analog signals, especially frequency division multiplexed signals, even a slight fluctuation in bias voltage can increase second order distortion (second order intermodulation distortion=IM2).
FIG. 14 is a diagram showing the relation between the bias voltage applied to the external optical modulator of FIG. 11 and the amount of second order distortion (hereinafter referred to as the amount of distortion) included in the optical signal outputted from the external optical modulator and caused by non-linearity thereof. As shown in FIG. 14, the amount of distortion exhibits a symmetric characteristic with respect to an axis representing the optimal bias voltage (Vb in the drawing). The amount of distortion becomes minimum when the bias voltage is equal to the optimal bias voltage, while surging when shifted therefrom even by a slightest amount.
The relation between the bias voltage and the amount of distortion is described below by using equations. When an analog signal provided to the external optical modulator has two frequencies, power of an output light from the external optical modulator can be represented by the following equation (10)                               P          out                =                              1            +                          cos              ⁡                              (                                                                            φ                                              D                        ⁢                                                  xe2x80x83                                                ⁢                        C                                                              ⁡                                          (                      V                      )                                                        +                                      m                    ⁢                                          xe2x80x83                                        ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                          ω                      1                                        ⁢                    t                                    +                                      m                    ⁢                                          xe2x80x83                                        ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                          ω                      2                                        ⁢                    t                                                  )                                              =                      1            +                          cos              ⁢                              xe2x80x83                            ⁢                                                                    φ                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    V                    )                                                  ⁡                                  [                                                                                                                                                                        J                              0                              2                                                        ⁡                                                          (                              m                              )                                                                                +                                                      2                            ⁢                                                                                          J                                1                                2                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                          {                                                                                                                                    sin                                    ⁡                                                                          (                                                                                                                        ω                                          1                                                                                +                                                                                  ω                                          2                                                                                                                    )                                                                                                        ⁢                                  t                                                                +                                                                                                      sin                                    ⁡                                                                          (                                                                                                                        ω                                          1                                                                                -                                                                                  ω                                          2                                                                                                                    )                                                                                                        ⁢                                  t                                                                                            }                                                                                +                                                                                                                                                                                          2                            ⁢                                                                                          J                                0                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                                                          J                                2                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                          {                                                                                                cos                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  2                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      ω                                    1                                                                    ⁢                                  t                                                                +                                                                  cos                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  2                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      ω                                    2                                                                    ⁢                                  t                                                                                            }                                                                                +                                                                                                                                                              2                          ⁢                                                                                    J                              2                              2                                                        ⁡                                                          (                              m                              )                                                                                ⁢                                                      {                                                                                          cos                                ⁢                                                                  xe2x80x83                                                                ⁢                                2                                ⁢                                                                  (                                                                                                            ω                                      1                                                                        +                                                                          ω                                      2                                                                                                        )                                                                ⁢                                t                                                            +                                                              cos                                ⁢                                                                  xe2x80x83                                                                ⁢                                2                                ⁢                                                                  (                                                                                                            ω                                      1                                                                        -                                                                          ω                                      2                                                                                                        )                                                                ⁢                                t                                                                                      }                                                                                                                                ]                                                      -                          sin              ⁢                              xe2x80x83                            ⁢                                                                    φ                    DC                                    ⁡                                      (                    V                    )                                                  ⁡                                  [                                                                                                                                          2                            ⁢                                                                                          J                                0                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                                                          J                                1                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                          {                                                                                                sin                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      ω                                    1                                                                    ⁢                                  t                                                                +                                                                  sin                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                                                      ω                                    2                                                                    ⁢                                  t                                                                                            }                                                                                +                                                                                                                                                                                          2                            ⁢                                                                                          J                                1                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                                                          J                                2                                                            ⁡                                                              (                                m                                )                                                                                      ⁢                                                          {                                                                                                                                    sin                                    ⁡                                                                          (                                                                                                                        ω                                          1                                                                                +                                                                                  2                                          ⁢                                                                                      ω                                            2                                                                                                                                                              )                                                                                                        ⁢                                  t                                                                +                                                                                                      sin                                    ⁡                                                                          (                                                                                                                        2                                          ⁢                                                                                      xe2x80x83                                                                                    ⁢                                                                                      ω                                            1                                                                                                                          +                                                                                  ω                                          2                                                                                                                    )                                                                                                        ⁢                                  t                                                                                            }                                                                                +                                                                                                                                                              2                          ⁢                                                                                    J                              1                                                        ⁡                                                          (                              m                              )                                                                                ⁢                                                                                    J                              2                                                        ⁡                                                          (                              m                              )                                                                                ⁢                                                      {                                                                                                                            sin                                  ⁡                                                                      (                                                                                                                  2                                        ⁢                                                                                  xe2x80x83                                                                                ⁢                                                                                  ω                                          1                                                                                                                    +                                                                              ω                                        2                                                                                                              )                                                                                                  ⁢                                t                                                            +                                                                                                sin                                  ⁡                                                                      (                                                                                                                  2                                        ⁢                                                                                  ω                                          2                                                                                                                    +                                                                              ω                                        1                                                                                                              )                                                                                                  ⁢                                t                                                                                      }                                                                                                                                ]                                                                                        (        10        )            
where xcfx891 and xcfx892 are angular frequencies of the analog signal.
In the above equation (10), the term including xcfx891 or xcfx892 represents the analog signal, while the other terms represent distortion components caused by non-linearity of the external optical modulator. Here, the ratios of IM2 and IM3 (third order intermodulation distortion) to the analog signal are represented by the following equations (11) and (12), respectively.                                                                         IM                2                            =                              20                ⁢                                  xe2x80x83                                ⁢                log                ⁢                                  {                                      2                    ⁢                                                                  J                        0                                            ⁡                                              (                        m                        )                                                              ⁢                                                                  J                        1                                            ⁡                                              (                        m                        )                                                              ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                                                                            φ                                                      D                            ⁢                                                          xe2x80x83                                                        ⁢                            C                                                                          ⁡                                                  (                          V                          )                                                                    /                      2                                        ⁢                                                                  J                        1                        2                                            ⁡                                              (                        m                        )                                                              ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          φ                                              D                        ⁢                                                  xe2x80x83                                                ⁢                        C                                                                                                                                                                    =                              20                ⁢                                  xe2x80x83                                ⁢                log                ⁢                                  {                                                                                                              J                          1                                                ⁡                                                  (                          m                          )                                                                    ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                                                        φ                                                      D                            ⁢                                                          xe2x80x83                                                        ⁢                            C                                                                          ⁡                                                  (                          V                          )                                                                                                                                                              J                          0                                                ⁡                                                  (                          m                          )                                                                    ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                                                                        φ                                                      D                            ⁢                                                          xe2x80x83                                                        ⁢                            C                                                                          ⁡                                                  (                          V                          )                                                                                                      }                                                                                        (        11        )                                                                                    IM                3                            =                              20                ⁢                                  xe2x80x83                                ⁢                log                ⁢                                  {                                      2                    ⁢                                                                  J                        2                                            ⁡                                              (                        m                        )                                                              ⁢                                                                  J                        1                                            ⁡                                              (                        m                        )                                                              ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                                                                            φ                                                      D                            ⁢                                                          xe2x80x83                                                        ⁢                            C                                                                          ⁡                                                  (                          V                          )                                                                    /                      2                                        ⁢                                                                  J                        1                                            ⁡                                              (                        m                        )                                                              ⁢                                                                  J                        0                                            ⁡                                              (                        m                        )                                                              ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                                                  φ                                                  D                          ⁢                                                      xe2x80x83                                                    ⁢                          C                                                                    ⁡                                              (                        V                        )                                                                              }                                                                                                        =                              20                ⁢                                  xe2x80x83                                ⁢                log                ⁢                                  {                                                                                    J                        2                                            ⁡                                              (                        m                        )                                                              /                                                                  J                        0                                            ⁡                                              (                        m                        )                                                                              }                                                                                        (        12        )            
As evident from the above equations (11) and (12), IM2 depends on the bias voltage and a phase modulation factor, while IM3 on the phase modulation factor. On the other hand, in the initial state, the bias voltage applied to the external optical modulator is set to the optimal bias voltage Vb. That is, the relation between the bias voltage and the phase satisfies the following equation (13).                                           φ            DC                    ⁡                      (                          V              b                        )                          =                  π          2                                    (        13        )            
Here, as can be seen from the above equation (11), IM2 does not occur.
Thereafter, however, the relation between the bias voltage and the phase fails to satisfy the above equation (13) due to a DC-drift characteristic of the external optical modulator. Here, a phase shift due to DC drift and the amount of distortion resulting therefrom are calculated in the following manner.
When the bias voltage V is shifted from the optimal bias voltage Vb by V, xcfx86DC can be represented by the following equation (14).                                           φ            DC                    ⁡                      (                                          V                b                            ⁢                              xe2x80x83                            -                              xe2x80x83                            ⁢                              Δ                ⁢                                  xe2x80x83                                ⁢                V                                      )                          =                              π            2                    ⁢                      xe2x80x83                    ⁢                      (                          1              ⁢                              xe2x80x83                            -                              xe2x80x83                            ⁢                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  V                                                  V                  π                                                      )                                              (        14        )            
where Vxcfx80 represents a switching voltage of the external optical modulator.
The above equation (14) can be represented by using a phase shift xcex94x (%) as the following equation (15).                                           φ            DC                    ⁡                      (                          Δ              ⁢                              xe2x80x83                            ⁢              x                        )                          =                              π            2                    ⁢                      xe2x80x83                    ⁢                      (                          1              ⁢                              xe2x80x83                            -                              xe2x80x83                            ⁢                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  x                                100                                      )                                              (        15        )            
By substituting the equation (15) into the above equation (11), IM2 and CSO (composite second order distortion) with respect to the shift in phase of the bias voltage from the optimal bias voltage are calculated. In these calculations, m=0.04. To convert IM2 into CSO, the maximum composite number is taken as 60 at the time of 60 ch transmission for power addition. The calculation results are shown in FIG. 15.
At analog 60-ch transmission, required technical specifications are that CSO should be below xe2x88x9260 dBc. To satisfy such requirement, as evident from FIG. 15, the shift in the bias voltage from the optimal bias voltage should be limited to approximately xc2x10.03% at maximum. Such accurate control cannot be made by monitoring changes in the average power of the optical signal.
Therefore, an object of the present invention is to provide an optical transmission apparatus including an external optical modulator that modulates an optical carrier from a light source with an electrical signal. The optical transmission apparatus according to the present invention is capable of making a bias voltage applied to the external optical modulator accurately follow a shift in the optimal bias voltage caused by DC drift. As a result, even if DC drift occurs due to variations with time or temperature, a change in the average power of the optical signal outputted from the external optical modulator and an increase in distortion included in the optical signal can be suppressed. Thus, the optical transmission apparatus with a stable transmission characteristic can be achieved.
The present invention has the following features to achieve the object above.
A first aspect of the present invention is directed to an optical transmission apparatus for externally modulating an optical carrier with an electrical signal for transmission. The apparatus comprises a light source for outputting the optical carrier an external optical modulator for modulating the optical carrier outputted from the light source with the electrical signal; a bias voltage applier for applying a bias voltage to the external optical modulator; and a bias voltage controller for controlling the bias voltage applied by the bias voltage applier to the external optical modulator based on an amount of second order distortion included in an optical signal from the external optical modulator and caused by non-linearity thereof.
In the above first aspect, the bias voltage applied to the external optical modulator (hereinafter referred to as applied bias voltage) is controlled based on the amount of second order distortion included in the optical signal from the external optical modulator and caused by non-linearity thereof. Therefore, the applied bias voltage can be made to more accurately follow the shift in the optimal bias voltage due to DC drift. As a result, even if DC drift occurs due to variations with time or temperature, it is possible to suppress a shift in the average power of the optical signal outputted from the external optical modulator and an increase in distortion included in the optical signal. Thus, an optical transmission apparatus with a stable transmission characteristic can be achieved.
Here, a shift in distortion with respect to a shift in bias voltage is described by using equations. Second order distortion (IM2) is represented by the above equation (11), and a value of an antilogarithm thereof is represented by the following equation (16).                               IM          2                =                                            (                                                J                  1                                                  J                  0                                            )                        2                    ⁢                                    {                                                cos                  ⁢                                      xe2x80x83                                    ⁢                                                            φ                      DC                                        ⁡                                          (                      V                      )                                                                                        sin                  ⁢                                      xe2x80x83                                    ⁢                                                            φ                      DC                                        ⁡                                          (                      V                      )                                                                                  }                        2                                              (        16        )            
By partial differentiation of the above equation (16), the shift in IM2 with respect to the shift in bias voltage can be obtained as shown in the following equation (17).                                                                         dIM                2                            =                                                                    (                                                                  J                        1                                                                    J                        0                                                              )                                    2                                ⁢                                                                            cos                      ⁢                                              xe2x80x83                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                    ⁢                                              sin                        2                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                    ⁢                                              2                                                  π                          ⁢                                                      xe2x80x83                                                    ⁢                                                      V                            π                                                                                              ⁢                      dV                                        -                                          2                      ⁢                                              cos                        2                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                    ⁢                                              2                                                  π                          ⁢                                                      xe2x80x83                                                    ⁢                                                      V                            π                                                                                              ⁢                      dV                                                                                                  (                                              sin                        ⁢                                                  xe2x80x83                                                ⁢                                                                              φ                            DC                                                    ⁡                                                      (                            V                            )                                                                                              )                                        3                                                                                                                          =                                                2                                      π                    ⁢                                          xe2x80x83                                        ⁢                                          V                      π                                                                      ⁢                                                      (                                                                  J                        1                                                                    J                        0                                                              )                                    2                                ⁢                                                                            cos                      ⁢                                              xe2x80x83                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                    ⁢                                              sin                        2                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                                      -                                          2                      ⁢                                              cos                        3                                            ⁢                                                                        φ                          DC                                                ⁡                                                  (                          V                          )                                                                                                                                                (                                              sin                        ⁢                                                  xe2x80x83                                                ⁢                                                                              φ                            DC                                                    ⁡                                                      (                            V                            )                                                                                              )                                        3                                                  ⁢                dV                                                                        (        17        )            
Compared with the shift in IM2 with respect to the shift in bias voltage from the optimal bias voltage, the average power of the optical signal with respect to the same is approximately 0 as shown in the above equation (6). On the other hand, the shift in IM2 becomes infinite as shown in the above equation (17). This can be clearly understood if FIGS. 12 and 14 are compared with each other in the gradient of each curve in the vicinity of the optimal bias voltage. Therefore, the bias voltage can be controlled more accurately by monitoring the amount of distortion included in the optical signal than by monitoring the average power of the optical signal.
According to a second aspect of the present invention, in the first aspect, the bias voltage controller includes: an optical branching unit for branching the optical signal from the external optical modulator into two optical signals; an optical-electrical converter for converting one optical signal from the optical branching unit into an electrical signal; a distortion detector for detecting the amount of second order distortion included in the optical signal from the external optical modulator and caused by the non-linearity thereof by extracting a component in a specific band from the electrical signal provided by the optical-electrical converter and measuring a level of the component; and a bias voltage control circuit for controlling the bias voltage applied by the bias voltage applier to the external optical modulator so as to minimize the amount of second order distortion detected by the distortion detector.
In the second aspect, the applied bias voltage is controlled to minimize the amount of distortion.
According to a third aspect of the present invention, in the second aspect, the bias voltage control circuit increases or decreases the bias voltage applied by the bias voltage applier to the external optical modulator, and determines whether the second order distortion detected by the distortion detector is increased or decreased before and after increasing or decreasing the bias voltage, and further determines, based on a determination result, whether to increase or decrease the bias voltage next time.
Here, the amount of distortion exhibits a symmetric characteristic with respect to an axis representing the optimal bias voltage (refer to FIG. 14). Therefore, if the optimal bias voltage is shifted due to DC drift, it should be determined whether to increase or decrease the applied bias voltage.
Therefore, in the third aspect, the applied bias voltage is first increased or decreased. Then, it is determined whether the amount of distortion has been increased or decreased. Based on the determination result, it is determined whether to increase or decrease the bias voltage next time. More specifically, if the amount of distortion is decreased as the applied bias voltage is increased (or decreased), the bias voltage is allowed to be further increased (or decreased), and if increased, the bias voltage is controlled in reverse, that is, decreased (or increased) next time.
Alternatively, as in a fourth aspect of the present invention, which will be described later, the average power of the optical signal outputted from the external optical modulator is further detected. It may be determined, based on the optical average power, whether to increase or decrease the applied bias voltage. More specifically, if the bias voltage applied to the external optical modulator and the average power of the optical signal outputted therefrom has a relation as shown in FIG. 12, the applied bias voltage is increased when the optical average power is increased, while decreased when decreased.
Alternatively, in a fifth aspect of the present invention, which will be described later, if the external optical modulator has two output ports (first and second ports), the amount of second order distortion included in the optical signal from the second port is detected. The applied bias voltage is controlled so that the detected amount of distortion agrees with a reference value. The reference value is, preferably as in a sixth aspect, a value of the amount of distortion detected by the distortion detector (the amount of distortion included in an optical signal from the second port side) when the bias voltage for minimizing the amount of second order distortion included in an optical signal from the first port (the optimal bias voltage in the first port side) is applied to the external optical modulator.
According to the fourth aspect, in the second aspect, the bias voltage controller further includes an optical power detector for detecting average optical power of the optical signal from the external optical modulator by measuring electrical power of the electrical signal from the optical-electrical converter, and the bias voltage control circuit determines, based on the average optical power detected by the optical power detector, whether to increase or decrease the bias voltage applied by the bias voltage applier to the external optical modulator.
According to the fifth aspect, in the first aspect, the external optical modulator includes: two waveguides for branching the optical carrier from the light source into two optical signals for guiding; an optical coupler for coupling the optical signals guided by the waveguides; and first and second ports for outputting the two optical signals from the optical coupler. Also, the bias voltage controller includes: an optical-electrical converter for converting the optical signal from the second port into an electrical signal; a distortion detector for detecting an amount of second order distortion included in the optical signal from the second port and caused by non-linearity of the external optical modulator by extracting a component in a specific band from the electrical signal outputted from the optical-electrical converter and measuring a level of the component; and a bias voltage control circuit for controlling the bias voltage applied by the bias voltage applier to the external optical modulator so that the amount of second order distortion detected by the distortion detector agrees with a previously-stored reference value.
In the above fourth and fifth aspects, whether to increase or decrease the applied bias voltage can be quickly recognized. Therefore, the applied bias voltage can be made to follow the shift in the optimal bias voltage due to DC drift quickly and accurately.
Note that in the fourth aspect, whether to increase or decrease the applied bias voltage is determined based on an increase or decrease in the average power of the output light. On the other hand, in the fifth aspect, this is determined based on the amount of distortion in the second port side. Therefore, only the amount of distortion in the second port side is required to be monitored, and thus the apparatus can be made simple in structure (the bias voltage control process can be simpler), compared with the apparatus of the fourth aspect.
According to the sixth aspect, in the fifth aspect, when the bias voltage applier applies to the external optical modulator the bias voltage that can minimize an amount of second order distortion included in the optical signal outputted from the first port and caused by non-linearity of the external optical modulator, the bias voltage control circuit stores the minimized amount of second order distortion detected by the distortion detector as the reference value.
A seventh aspect is directed to, in an optical transmission apparatus comprising an external optical modulator that modulates an optical carrier from a light source with an electrical signal, a method of controlling a bias voltage applied to the external optical modulator. The method comprises measuring an amount of second order distortion included in an optical signal from the external optical modulator and caused by non-linearity thereof; and controlling the bias voltage applied to the external optical modulator so as to minimize the amount of second order distortion measured in the distortion measuring step.
According to an eighth aspect, in the seventh aspect, the bias voltage control method further comprises a step of detecting average optical power of the optical signal from the external optical modulator, wherein the bias voltage controlling step includes determining, based on the optical average power detected in the optical power detecting step, whether to increase or decrease the bias voltage applied to the external optical modulator.
According to a ninth aspect, in the seventh aspect, the external optical modulator includes: two waveguides for branching the optical carrier from the light source into two optical signals for guiding; an optical coupler for coupling the optical signals guided by the waveguides; and first and second ports provided to the optical coupler for outputting the two optical signals. Also, the bias voltage controlling step includes detecting an amount of second order distortion included in the optical signal from the second port and caused by non-linearity of the external optical modulator; and controlling the bias voltage applied to the external optical modulator so that the amount of second order distortion detected in the distortion detecting step agrees with a previously-stored reference value.
According to a tenth aspect, in the ninth aspect, the bias voltage control step includes storing the amount of second order distortion detected in the distortion detecting step as the reference value in an initial state in which the bias voltage is applied to the external optical modulator so as to minimize the amount of second order distortion included in an optical signal outputted from the first port and caused by non-linearity of the external optical modulator.
These and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.